What is the integral of 1/(sqrt(x)\sqrt[3]{x)} ?

The integral of 1/(sqrt(x)\sqrt[3]{x)} is 6\sqrt[6]{x}+C

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integral of 1/(sqrt(x)\sqrt[3]{x)}

\int \frac{1}{x 3 x} d x

6 6 x + C

Solution steps

\int \frac{1}{x 3 x} d x

Simplify

\frac{1}{x 3 x} : \frac{1}{x ^{\frac{5}{6}}}

= \int \frac{1}{x ^{\frac{5}{6}}} d x

Apply the Power Rule

: 6 x^{\frac{1}{6}}

= 6 x^{\frac{1}{6}}

Apply radical rule:

a^{\frac{1}{n}} = n a

= 6 6 x

Add a constant to the solution

= 6 6 x + C

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What is the integral of 1/(sqrt(x)\sqrt[3]{x)} ?
The integral of 1/(sqrt(x)\sqrt[3]{x)} is 6\sqrt[6]{x}+C